Algebraic patching over complete domains

We extend the method of algebraic patching due to Haran-Jarden-Völklein from complete absolute valued fields to complete domains. We apply the extended method to reprove a result of Lefcourt obtained by formal patching — every finite group is regularly realizable over the quotient field of a complete domain.     

Interferometry using binary holograms without high order diffraction effects

We describe a technique for a phase-stepping interferometer based on programmable binary phase holograms, particularly useful for optical testing of aspheric or free-form surfaces. It is well-known that binary holograms can be used to generate reference surfaces for interferometry, but a major problem is that cross talk from higher diffraction orders and aliasing can reduce the fidelity of the system. Here, we propose a new encoding technique which improves the accuracy of the technique and demonstrate its implementation using a binary liquid crystal spatial light modulator.     

Polymer-anchored peroxo compounds of vanadium(V) and molybdenum(VI): synthesis, stability, and their activities with alkaline phosphatase and catalase

We generated a series of new polymer-bound peroxo complexes of vanadium(V) and molybdenum(VI) of the type [VO(O(2))(2)(sulfonate)]-PSS [PSS = poly(sodium 4-styrene sulfonate)] (PV(3)), [V(2)O(2)(O(2))(4)(carboxylate)VO(O(2))(2)(sulfonate)]-PSSM [PSSM = poly(sodium styrene sulfonate-co-maleate)] (PV(4)), [Mo(2)O(2)(O(2))(4)(carboxylate)]-PA [PA = poly(sodium acrylate)] (PMo(1)), [MoO(O(2))(2)(carboxylate)]-PMA [PMA = poly(sodium methacrylate)] (PMo(2)), and [MoO(O(2))(2)(amide)]-PAm [PAm = poly(acrylamide)] (PMo(3)) by reacting V(2)O(5) (for PV(3) and PV(4)) or H(2)MoO(4) (for PMo(1), PMo(2), and PMo(3)) with H(2)O(2) and the respective water-soluble macromolecular ligand at pH 5-6. The compounds were characterized by elemental analysis (CHN and energy-dispersive X-ray spectroscopy), spectral studies (UV-vis, IR, (13)C NMR, (51)V NMR, and (95) Mo NMR), thermal (TGA) as well as scanning electron micrographs (SEM), and EDX analysis. It has been demonstrated that compounds retain their structural integrity in solutions of a wide range of pH values and are approximately 100 times weaker as substrate to the enzyme catalase relative to H(2)O(2), its natural substrate. The effect of the title compounds, along with previously reported compounds [V(2)O(2)(O(2))(4)(carboxylate)]-PA (PV(1)) and [VO(O(2))(2)(carboxylate)]-PMA (PV(2)) on rabbit intestine alkaline phosphatase (ALP) has been investigated and compared with the effect induced by the free diperoxometallates viz. Na[VO(O(2))(2)(H(2)O)] (DPV), [MoO(O(2))(2)(glycine)(H(2)O)] (DMo(1)), and [MoO(O(2))(2)(asparagine)(H(2)O)] (DMo(2)). It has been observed that although all the compounds tested are potent inhibitors of the enzyme, the polymer-bound and neat complexes act via distinct mechanisms. Each of the macromolecular compounds is a classical noncompetitive inhibitor of ALP. In contrast, the action of neat pV and heteroligand pMo compounds on the enzyme function is consistent with a mixed type of inhibition.     

Premicellar and micelle formation behavior of aqueous anionic surfactants in the presence of triphenylmethane dyes: protonation of dye in ion pair micelles

The premicellar and micelle formation behaviors of four cationic triphenylmethane dyes, viz, Pararosaniline (RN), Crystal violet (CV), Ethyl violet (EV), and Malachite green (MG), in aqueous anionic surfactant solutions of sodium dodecyl sulfate (SDS), sodium dodecyl benzene sulfonate (SDBS), and sodium dodecyl sulfonate (SDSN) have been studied by spectral and surface tension measurements. The study was carried out within a pH range where the dyes are stable in their quinoid forms. The dyes have been found to form dye–surfactant ion pairs (DSIPs) with the surfactants, at the surfactant concentrations well below their critical micelle concentration, CMC*. The DSIPs behave like nonionic surfactants and form an air–water interfacial monolayer. The DSIPs have a lower critical micelle concentration (CMC_IP), greater efficiency, and lower effectiveness than the corresponding pure surfactants. As the surfactant concentration is increased below the CMC*, the DSIPs start forming micelles of their own where the dye gets protonated and exists as a protonated dye–surfactant ion pair (PDSIP) in the ion pair micelles. As the concentration of the surfactant exceeds the CMC* of the pure surfactant, the protonation reverses gradually with the dye remaining in the micelles in solubilized form and the DSIPs in the air–water interfacial monolayer are replaced by pure surfactants. The distorted helical isomeric form (isomer B) of the dyes is favored in the PDSIPs. Copyright © 2009 John Wiley & Sons, Ltd.     

Some results on a special case of a general continued fraction of Ramanujan

We derive a new special case C(q) of a general continued fraction recorded by Ramanujan in his Lost Notebook. We give a representation of the continued fraction C(q) as a quotient of Dedekind eta-function and then use it to prove modular identities connecting C(q) with each of the continued fractions \(C(-q)\), \(C(q^{2})\), \(C(q^{3})\), \(C(q^{5})\), \(C(q^{7})\), \(C(q^{11})\), \(C(q^{13})\) and \(C(q^{17})\). We also prove general theorems for the explicit evaluation of the continued fraction C(q) by using Ramanujan’s class invariants.     

Visible-Light Augmented Lithium Storage Capacity in a Ruthenium(II) Photosensitizer Conjugated with a Dione-Catechol Redox Couple

Controlling redox activity of judiciously appended redox units on a photo-sensitive molecular core is an effective strategy for visible light energy harvesting and storage. The first example of a photosensitizer - electron donor coordination compound in which the photoinduced electron transfer step is used for light to electrical energy conversion and storage is reported. A photo-responsive Ru-diimine module conjugated with redox-active catechol groups in [Ru(II)(phenanthroline-5,6-diolate)₃]⁴⁻ photosensitizer can mediate photoinduced catechol to dione oxidation in the presence of a sacrificial electron acceptor or at the surface of an electrode. Under potentiostatic condition, visible light triggered current density enhancement confirmed the light harvesting ability of this photosensitizer. Upon implementation in galvanostatic charge-discharge of a Li battery configuration, the storage capacity was found to be increased by 100 %, under 470 nm illumination with output power of 4.0 mW/cm⁻². This proof-of-concept molecular system marks an important milestone towards a new generation of molecular photo-rechargeable materials.     

Selective and solventless oxidation of organic sulfides and alcohols using new supported molybdenum (VI) complex in microwave and conventional methods

A new dioxo-molybdenum (VI) complex supported on functionalized Merrifield resin ( MR-Mo ) has been synthesized and characterized by elemental, scanning electron mcroscopy, energy-dispersive X-ray analysis, TGA, Brunauer–Emmett–Teller method, powder-X-ray diffraction, Fourier transform infrared, X-ray photoelectron spectroscopy and DRS–UV–vis analysis. The virgin Merrifield resin ( MR ) was functionalized by carbonylation followed by Schiff base formation with ethanolamine ( MR-SB ). Experimental data showed that the Schiff base coordinated with the MoO₂²⁺ moiety via O- and N-atoms. The catalytic activity of MR-Mo was explored under solventless conditions toward the oxidation of organic sulfides and alcohols using 30% aqueous H₂O₂ as oxidant. The oxidation reactions were conducted under microwave and conventional methods. The microwave-assisted oxidation reactions were found to be many times faster than the conventional methods. The oxidation reactions were selective and formed sulfoxides or aldehydes as the sole product with superior TOF values among the molybdenum (VI)-based complexes. Besides these, the MR-Mo was purely heterogeneous in nature and can be recycled for at least five reaction cycles without the loss of catalytic efficiency and product selectivity.     

Resolution of racemic 1-arylethyl acetates by Pseudomonas fluorescens in the presence of a surfactant

The Pseudomonasfluorescens RRLJ 134 strain efficiently resolved (R/S)-1-arylethyl acetates into S-(−)-1-arylethyl acetates and R-(+)-1-arylethanol in the presence of the surfactant Tween-80. The surfactant reverses the enantioselectivity compared to the surfactant free medium.     

Galois theory over complete local domains

Complete local domains play an important role in commutative algebra and algebraic geometry, and their algebraic properties were already described by Cohen’s structure theorem in 1946. However, the Galois theoretic properties of their quotient fields only recently began to unfold. In 2005 Harbater and Stevenson considered the two dimensional case. They proved that the absolute Galois group of the field K((X, Y)) (where K is an arbitrary field) is semi-free. In this work we settle the general case, and prove that if R is a complete local domain of dimension exceeding 1, then the quotient field of R has a semi-free absolute Galois group.     

Studies on 2,1 -benzisoxazoles and related heterocycles. Reaction of diazomethane with 6-nitro-2,1-benzisoxazoles and nitrobenzofurazan oxides

Some 7-melhyl-substituted-2,1-benzisoxazoles and cyclopropanobenzofurazan oxides are synthesized and characterized by their elemental and spectral analyses.